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10.3 Forces and Braking

GCSE Physics · AQA · Chapter 10: Force and Motion

A free GCSE Physics lesson for AQA (8463) from OBA School: driving and resistive forces, stopping distance, reaction time, braking distance and braking force. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Explain why the resultant force on a vehicle moving at a steady velocity is zero
  • Use stopping distance = thinking distance + braking distance, and calculate thinking distance from speed and reaction time
  • Describe the factors that affect reaction time and braking distance, and how reaction time can be measured
  • Explain how the brakes reduce the kinetic energy of a vehicle and why large decelerations are dangerous
  • (Higher tier) estimate the deceleration and braking force of a vehicle using v² − u² = 2 a s and F = m a

Key words

  • Driving force: The forward force on a vehicle produced by its engine or motor.
  • Resistive forces: Forces that oppose motion, mainly air resistance and friction.
  • Reaction time: The time between a driver seeing a hazard and starting to act, for example pressing the brake.
  • Thinking distance: The distance travelled during the driver’s reaction time.
  • Braking distance: The distance travelled while the braking force acts, until the vehicle stops.
  • Stopping distance: The total distance a vehicle travels from the moment the driver sees a hazard until it stops.
  • Deceleration: Negative acceleration: the rate at which velocity decreases, in m/s².

Forces on a moving vehicle

A vehicle’s engine provides a driving force. Resistive forces – mostly air resistance at high speeds, plus friction in moving parts – act against the motion. The driver uses the accelerator pedal to change the driving force.

  • Driving force = resistive forces: resultant force zero, constant velocity.
  • Driving force > resistive forces: the car accelerates.
  • Driving force < resistive forces (or brakes applied): the car decelerates.

Worked example: pulling away

A car of mass 1100 kg has a driving force of 3000 N and resistive forces of 800 N. Calculate its acceleration.
resultant force = 3000 − 800 = 2200 N; a = F ÷ m = 2200 ÷ 1100

Answer: a = 2.0 m/s²

Stopping distance

stopping distance = thinking distance + braking distance

During the reaction time the vehicle has not started to slow down, so:

thinking distance = speed × reaction time (thinking distance is directly proportional to speed)

Worked example: stopping from 25 m/s

A driver with a reaction time of 0.6 s is travelling at 25 m/s. The braking distance is 50 m.
thinking distance = 25 m/s × 0.6 s = 15 m
stopping distance = 15 m + 50 m

Answer: 65 m

Key fact: Compare 10 m/s and 20 m/s in the chart: doubling the speed doubles the thinking distance (6 m → 12 m) but makes the braking distance four times bigger (8 m → 32 m).

Reaction time

Typical reaction times are between about 0.2 s and 0.9 s. Reaction time, and so thinking distance, is increased by:

  • tiredness
  • alcohol and some drugs (including some medicines)
  • distractions, such as using a mobile phone, adjusting a sat-nav or talking to passengers

Measuring reaction time with a ruler. A partner holds a metre ruler vertically with the zero mark between your open finger and thumb, then lets go without warning. You catch it as fast as you can. The further it falls, the longer your reaction time. Repeat several times and take a mean. Because the ruler falls freely, the time can be found from t = √(2s ÷ g).

Worked example: ruler-drop result

A student catches the ruler after it has fallen 18 cm. Calculate her reaction time.
s = 0.18 m; t = √(2 × 0.18 ÷ 9.8) = √0.0367

Answer: t = 0.19 s

A computer test (click when the screen changes colour) measures reaction time more precisely, because there is no one judging when the ruler was dropped.

Braking distance and braking energy

Braking distance is increased by:

  • higher speed (the biggest effect)
  • wet or icy roads: less friction between tyres and road, so the brakes must be applied more gently to avoid skidding
  • worn tyres (less grip) or worn brakes (less braking force)
  • greater mass, for example a fully loaded van or a trailer

When the brakes are applied, friction between the brake pads and the discs does work on the wheels. This reduces the kinetic energy of the vehicle and transfers energy to the thermal store of the brakes, so their temperature rises.

work done by brakes = loss of kinetic energy: F × s = ½ m v²

Worked example: braking distance from energy

A 1200 kg car moving at 15 m/s brakes with a constant force of 6000 N. Calculate its braking distance.
Ek = ½ × 1200 × 15² = 135 000 J
s = Ek ÷ F = 135 000 ÷ 6000

Answer: s = 22.5 m

Doubling the speed makes the kinetic energy four times bigger, so with the same braking force the braking distance is four times longer. Very large decelerations are dangerous: the brakes can overheat, the wheels can lock and skid, the driver can lose control, and people inside are thrown forward with large forces.

Estimating deceleration and braking force (Higher tier)

For a vehicle that stops (v = 0) from initial speed u in braking distance s, the equation v² − u² = 2 a s gives:

a = −u² ÷ 2s (the minus sign shows a deceleration)

braking force: F = m a

Worked example: braking force on a car

A car of mass 1200 kg travelling at 20 m/s stops in a braking distance of 32 m.
a = −20² ÷ (2 × 32) = −400 ÷ 64 = −6.25 m/s²
F = m a = 1200 × 6.25 = 7500 N

Answer: deceleration 6.25 m/s²; braking force about 7.5 kN

Useful estimates: a car has a mass of roughly 1000–1500 kg; a fully loaded lorry about 40 000 kg. On a dry road a car can decelerate at about 6–7 m/s² without skidding. So braking forces range from several kilonewtons for a car to over 200 kN for a heavy lorry.

Exam tip: At a constant deceleration, braking distance ∝ (speed)². If speed goes up by a factor of 3, braking distance goes up by 3² = 9.

Common mistakes

  • Saying tiredness or alcohol increases the braking distance. They increase reaction time, so they increase the thinking distance.
  • Saying wet roads or worn tyres increase the thinking distance. They increase the braking distance.
  • Assuming that doubling the speed doubles the braking distance. It makes it about four times longer.
  • Forgetting to convert a reaction time in milliseconds to seconds (650 ms = 0.65 s).
  • Forgetting that the vehicle travels at full speed during the reaction time.

Revision questions

Try these, then check your answers below each one.

Question 1. A driver travelling at 20 m/s has a reaction time of 0.70 s. Calculate her thinking distance.

Answer: 14 m

Working: Thinking distance = 20 m/s × 0.70 s = 14 m.

Question 2. Which of these increases the thinking distance of a driver? (Choose from: A wet road surface, Worn tyres, Worn brake pads, Using a mobile phone while driving.)

Answer: Using a mobile phone while driving

Working: A distraction such as a phone increases the reaction time, so the thinking distance increases. Wet roads, worn tyres and worn brakes increase the braking distance.

Question 3. True or false? If a car’s speed doubles, its braking distance doubles.

Answer: False

Working: False. Kinetic energy is ½ m v², so doubling the speed gives four times the energy. With the same braking force, the braking distance is about four times longer.

Related lessons

Continue in the full course

This lesson is section 10.3 (AGCPH1003) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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